Experimental Study of the Leakage and Rotordynamic Coefficients of a Long Smooth Seal With Two-Phase, Mainly-Oil Mixtures

Abstract

Tests are conducted on a newly developed 2-phase annular seal stand (2PASS) at the Turbomachinery Laboratory of Texas A&M University. The test fluid is a mixture of silicone oil (PSF-5cSt) and air. Two spargers are used to produce mainly-oil mixtures by injecting air bubbles into the oil flow. The test seal is a smooth annular seal with inner diameter D = 89.306 mm, length-to-diameter ratio L/D = 0.65, and radial clearance Cr = 0.188 mm. Tests are performed with inlet gas-volume-fraction GVF = 0%, 2%, 4%, 6%, and 10%, rotor speed ω = 5, 7.5, 10, and 15 krpm, inlet temperature Ti = 39.4 °C, exit pressure Pe = 6.9 bars, and pressure drop PD = 31, 37.9, and 48.3 bars. The test seal is centered, and there is no intentional prerotation of the fluid at the seal inlet. The complex dynamic stiffness coefficients of the test seal are measured and fitted by the frequency-independent stiffness Kij, damping Cij, and virtual-mass Mij coefficients. Test results show that adding air into the oil flow does not change the seal’s mass flow leakage ṁ discernibly but significantly impacts the seal’s rotordynamic characteristics. Some planned 5 krpm cases with low inlet GVFs at PD = 31 and 37.9 bars are not accomplished due to stator instabilities, which are likely caused by negative stiffness of the test seals. For ω = 5 krpm when PD = 31 and 37.9 bars, direct stiffness K decreases from positive to negative as inlet GVF decreases. For all PDs and speeds, K increases as inlet GVF increases from zero to 10% except for 6% ≤ inlet GVF ≤ 10% when PD = 48.3 bars, where K decreases as inlet GVF increases. The K increment will increase a pump rotor’s natural frequency and critical speed. Increasing the rotor’s natural frequency would also increase the onset speed of instability (OSI) and improve the stability of the rotor. Adding air into the oil flow has little effect on cross-coupled stiffness k and direct damping C. Increasing inlet GVF has negligible effects on direct virtualmass M when ω ≤ 10 krpm and PD ≤ 37.9 bars, but generally decreases M when ω = 15 krpm or PD = 48.3 bars. Increasing inlet GVF has little effect on effective damping Ceff and does not change the seal’s resultant stabilizing force discernibly. Ceff = C − k/ω + mqω, where mq is the cross-coupled virtual-mass. Test results are compared to predictions from San Andrés’s [1] model. The model is based on a bulk-flow model and the Moody friction formula assuming that the liquid-gas mixture is isothermal and homogenous. The model reasonably predicts ṁ, C, and Ceff. All predicted K values are positive, while measured K values are negative for some test cases. Predicted k values are close to measurements when ω = 5 krpm and are larger than test results when 7.5 ≤ ω ≤ 15 krpm. M predictions are smaller than measurements, and the discrepancy between predicted and measured M values generally increases as inlet GVF increases.